I don’t have an iPhone upgrade plan. Is it possible to give my iPhone 8 as part of the payment to have an iPhone X?

No.

See here: Trade in with Apple GiveBack - Apple

No. Currently the trade in program is not accepting iPhone 8.

However since a new iPhone is likely to be released in September, I would wait and upgrade then through the Trade-In program as its surely going to be an option once its released.

Yes, you can use Apple Trade-In:

Trade in with Apple GiveBack - Apple

But you'd probably do better selling it privately.

Oops, ckuan is correct iPhone 8 is not listed.